The Doppler asymmetric spatial heterodyne spectroscopy is one of the primary techniques for measuring the upper atmospheric wind profile. In this work, the detailed derivation of the analytical expression of phase uncertainty was presented, including two significant parameters, fringe contrast and signal-to-noise ratio. The effectiveness of the re-parameterized analytical expression was proved using the numerical simulations and laboratory experiments, and both results are in good agreement with them from the analytical expression. Therefore, the re-parameterized analytical expression could be used to optimize the interferometer design and evaluating the instrument performance.